Geodesic
Normal solvability of a~class of differential equations of infinite order
Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 371-399

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In this article we study a differential equation of infinite order with polynomial coefficients \begin{equation} Ly\equiv\sum^\infty_{k=1}P_k(x)y^k(x)=f(x),\qquad P_k(x)=\sum^{n_k}_{s= 0}a_s^k x^s, \end{equation} where $\varlimsup_{k\to\infty}\frac{n_k}k=\alpha1$. Under given conditions on the coefficients $a_s^k$, normal solvability of equation $(1)$ is established in the class of entire functions $[1-\alpha,Q]$, where $0$ and $Q$ is determined by the coefficients $a_s^k$. Bibliography: 10 titles. 
@article{SM_1971_13_3_a3,
     author = {Yu. F. Korobeinik and O. V. Epifanov},
     title = {Normal solvability of a~class of differential equations of infinite order},
     journal = {Sbornik. Mathematics},
     pages = {371--399},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_13_3_a3/}
}
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Yu. F. Korobeinik; O. V. Epifanov. Normal solvability of a~class of differential equations of infinite order. Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 371-399. http://geodesic.mathdoc.fr/item/SM_1971_13_3_a3/